# Modal Analysis Essay

Extraction of the modal parameters from the response of the structure to vibration is an important step in SHM. Firstly, it gives to the engineers information about real dynamic behaviour of the structure. Secondly, designed model of the structure using computing technologies, FEM model, may be validated and optimized through comparison analytical and experimental modal parameters. The procedure developing the mathematical model of the structure on the basis of the experimental data is also known as system identification. The part of this procedure is the identification of the modal parameters of the system called modal analysis.

Modern modal analysis may be classified depending on excitation source of the

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It includes variety of techniques such as single-input-single-output (SISO), multiple input-multiple output (MIMO) techniques (Ewins DJ (2000) Modal testing: theory, practice and application, 2nd edn. Research Studies Press Ltd., Baldock, Heylen W, Lammens S, Sas P (1998) Modal analysis theory and testing. Katholieke Universiteit Leuven, Leuven). Deterministic knowledge of the input gives robust results in the mechanical, aerospace fields. However, it may be difficult and expensive to excite the large civil structures such as bridges by artificial force. The levels of vibration under operational conditions may exceed the artificially induced vibration in this case. Therefore, another area of modal analysis known as OMA, starting in the last decade of twentieth century, has focused attention of civil engineers. OMA provides the identification of modal parameters of the structure being exited by unknown ambient force. The input is assumed as a stochastic process, also known as white noise, in this case. However, sometimes ambient excitation may contain some dominant frequency components which could be easily confused with natural frequencies of the structure. The separation of the true modal parameters from erroneous ones should be done on the next step using various methods ( Jacobsen, N-J Separating Structural Modes and

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One is the LSCE approach which is the time domain counterpart of the LSCF estimator (Brown, D.L. & R.J. Allemang, R. Zimmerman & M. Mergeay: Parameter estimation techniques for modal analysis, SAE Paper, No. 790221, 1979).. This is two-stage method consisting of estimation of the correlation function in time domain following by modal parameter identification. Other low order method also known as Ibrahim time domain (ITD) process all function at once (Ibrahim SR, Mikulcik EC (1977) A method for the direct identification of vibration parameters from free response. Shock Vib Bull 47:183–196). Finally, Eigensystem realization algorithm (ERA) which is relies on the system realization theory (Juang and Pappa 1985). Generally, all these methods based on the idea that the cross-correlation function of two random responses of the structure can be expressed as a summation of decaying sinusoids having the characteristics similar to impulse response